Question: Express your answer as a mixed number simplified to lowest terms. $17\dfrac{1}{3}-5\dfrac{4}{5} = {?}$
Solution: Find a common denominator for the fractions: $= {17\dfrac{5}{15}}-{5\dfrac{12}{15}}$ Convert ${17\dfrac{5}{15}}$ to ${16 + \dfrac{15}{15} + \dfrac{5}{15}}$ So the problem becomes: ${16\dfrac{20}{15}}-{5\dfrac{12}{15}}$ Separate the whole numbers from the fractional parts: $= {16} + {\dfrac{20}{15}} - {5} - {\dfrac{12}{15}}$ Bring the whole numbers together and the fractions together: $= {16} - {5} + {\dfrac{20}{15}} - {\dfrac{12}{15}}$ Subtract the whole numbers: $=11 + {\dfrac{20}{15}} - {\dfrac{12}{15}}$ Subtract the fractions: $= 11+\dfrac{8}{15}$ Combine the whole and fractional parts into a mixed number: $= 11\dfrac{8}{15}$